Bialynicki-Birula theory, Morse-Bott theory, and resolution of singularities for analytic spaces
| Autor: | Feehan, Paul M. N. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | Our goal in this work is to develop aspects of Bialynicki-Birula and Morse-Bott theory that can be extended from the classical setting of smooth manifolds to that of complex analytic spaces with a holomorphic $\mathbb{C}^*$ action. We extend prior results on existence of Bialynicki-Birula decompositions for compact, complex K\"ahler manifolds to non-compact complex manifolds and develop functorial properties of the Bialynicki-Birula decomposition, in particular with respect to blowup along a $\mathbb{C}^*$-invariant, embedded complex submanifold. We deduce the existence of a Bialynicki-Birula decomposition for a $\mathbb{C}^*$-invariant, closed, complex analytic subspace of complex manifold with a $\mathbb{C}^*$ action; derive geometric consequences for the positivity of the Bialynicki-Birula nullity, co-index, and index at a fixed point; and we develop stronger versions of these results by applying resolution of singularities for analytic spaces. Comment: 196 pages, 5 figures, 334 bibliographic entries, draws on arXiv:2010.15789 with Thomas G. Leness for background material |
| Databáze: | arXiv |
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